Gravity and Motion and Time on the Earth Upward Bound

Forces in Nature l Terrestrial gravity l Celestial gravity l Strong Nuclear l Electrical l Magnetic l Weak Nuclear Gravity Electromagnetic

Laws of Gravity & Motion These allow us to ask and answer simple, fundamental questions Why does the Earth go round the Sun? How do we figure out what a planet is made up off? Why do we weigh less on the moon? Why does the Earth have an atmosphere while the moon does not? All due to Sir Issac Newton

Inertia l The tendency of body at rest to remain at rest, and one in motion to continue in motion l In the absence of forces, inertia keeps an object already in motion, in motion l Inertia is measured by mass l First demonstrated by Galileo

First Law of Motion a Review l A body at rest or a body in uniform motion in a straight line stays in its state unless acted on by a force l Circular orbits of bodies means there has to be a force acting on them

If a projectile moves fast enough the Earth’s surface will fall away from it so that it remains airborne (in orbit) Path is curved because gravity acts on ball Inertia keeps the body moving Gravity

Second Law of Motion l Motion is a change of position and consists of direction and speed l Uniform motion - constant velocity l Non-uniform motion - acceleration l All bodies orbiting the Sun are accelerating

Second Law of Motion l Two factors determine how a body accelerates Net Force – Sum of forces on the object Mass - the amount of matter an object contains (inertia) l The amount of acceleration (a) a mass (m) undergoes depends on the net force (F) F = ma

Third Law of Motion Why does the Earth go round the Sun? l “When two bodies interact they create equal and opposite forces on each other” l From F = ma we get a = F/m Acceleration a body feels is inversely proportional to its mass l Sun is more massive so it accelerates less, whereas the Earth accelerates more l The Sun moves due to gravity from the Earth, but not as much as the Earth does

Law of Gravity l To predict a body’s motion we need understand the force acting on it l For astronomical bodies this is Gravity l Newton’s Law of Gravity states “Every mass exerts a force of attraction on every other mass. The strength of the force is directly proportional to the product of the masses divided by the square of their separation” F grav =GMm/ r 2

How do we figure out what a planet is made of? l Orbital motion (orbital radius and velocity) yields information about mass l Lets consider A small body in a circular orbit around a more massive object First law - circular orbit means a force must be acting on the body

How do we figure out what a planet is made of? Second law F=ma can be used to show that this force is F = mv 2 /r Centripetal force- amount of force required to keep a planet in orbit l Centripetal force due to Gravity l F grav = GMm/r 2 = mv 2 /r  Orbital motion yields mass

How do we figure out what a planet is made of? l We can measure size (volume) remotely Distance and angular size yield size l This yields a density (mass/volume) which can be used to extract composition 3.5 g/cm 3  rocky 1 g/cm 3  gaseous

Surface Gravity Why do we weigh less on the Moon? l Weight is a measure of the force gravity l At the surface of a planet gravity accelerates bodies towards the center of the planet l Law of Gravity F = GMm/R 2 ; R is planet radius l The Moon has less mass  less weight

Escape Velocity Why does the Moon have no atmosphere? To escape the pull of gravity on a planet a critical speed, the escape velocity, must be exceeded

Escape Velocity Why does the Moon have no atmosphere? l The smaller the mass, the lower the escape velocity l Gas molecules in an atmosphere move fast l Smaller planets or bodies like the moon are less able to hold molecules of gas (atmosphere) around them

How long is a day? l Length of a day set by Earth’s rotation l But, sunrise to sunrise is not 24 hours l Different from one day to the next l Star rise to Star rise is constant but 4 minutes less than 24 hours l Sidereal vs. Solar days l Solar day is 4 minutes longer

“Extra” rotation is 360/365.25° or ~1° The 1° takes 1/ days or 4 min 1 year of extra rotations is one full circle